I wouldn't, and it's exactly why I opted out of a group when we were living in the Philadelphia area. It's ridiculous. For awhile now, the AKC has permitted dogs to pass the Canine Good Citizen test on a harness as long as it is not the corrective type, so there is really no excuse.
I'm so sorry you've found yourself in this situation, especially when you want to do something so wonderful for others with your pup. I hope you can find a group that will accommodate harness use.
No one has been able to give me a rationale for why it has to be that way. The group I mentioned above simply told me she had chihuahuas that walked on collars, and they were all fine.
What does that have to do with me not wanting to put my dog in a potentially dangerous situation? Good luck!